Re: Paired t test vs. 2-way ANOVA

From: Gang Chen (gangchen_at_mail.nih.gov)
Date: 08/26/04 

Date: Wed, 25 Aug 2004 22:28:49 -0400

Some correction:

> Actually I just found out that s^2 = 2*MSAB for paired t test and 2-way
> ANOVA, so the two t tests are indeed equivalent.
>
> Now my question mutates to another comparison between two samples from two
> different populations:
>
> (1) Run unpaired t test
>
> (2) Run 2-way ANOVA with first factor (fixed) being two groups, second
> (random) subjects nested within the first factor.
>
> Which one is more powerful? Why?
>
> Gang
>
> "Gang Chen" wrote in message
> > Suppose there are two samples (with same sample size n) of data from the
> > same subjects. It seems that there are two approaches to test whether
the
> > means of the two samples are
> > the same:
> >
> > (1) run a paired t test on the two samples
> >
> > t = (Y_1.-Y_2.)/[sqrt(s^2/n)], where n is sample size, and s^2 is the
> > common variance = SUM(Y_1i - Y_2i - Y_1.+Y_2.)^2/(n-1)
> >
> > (2) run 2-way ANOVA with two factors, one factor fixed with two levels
> while
> > the other factor (subject) being random (no repeated measure for each
> cell):
> >
> > t = (Y_1.-Y_2.)/sqrt(MSAB*2/n), where n is the levels of the second
factor
> > (subject)
> >
> > I thought that (2) would be more powerful since the interaction between
> the
> > two factors are accounted for while the interaction is assumed to be 0
in
> > (1), but I could not prove it by comparing s^2 and MSAB algebraically.
> Which
> > analysis is more appropriate? Which is more statistically powerful?
> >
> > Thanks,
> > Gang
>
>

Relevant Pages

  • Re: Paired t test vs. 2-way ANOVA
    ... ANOVA, so the two t tests are indeed equivalent. ... Now my question mutates to another comparison between two samples from two ... different populations: ... "Gang Chen" wrote in message ...
    (sci.stat.math)
  • Re: Paired t test vs. 2-way ANOVA
    ... ANOVA, so the two t tests are indeed equivalent. ... Now my question mutates to another comparison between two samples from two ... different populations: ... "Gang Chen" wrote in message ...
    (sci.stat.edu)
  • Re: Paired t test vs. 2-way ANOVA
    ... > ANOVA, so the two t tests are indeed equivalent. ... > Now my question mutates to another comparison between two samples from two ... Which is more statistically powerful? ...
    (sci.stat.math)
  • Paired t test vs. 2-way ANOVA
    ... run 2-way ANOVA with two factors, one factor fixed with two levels while ... the other factor being random (no repeated measure for each cell): ... but I could not prove it by comparing s^2 and MSAB algebraically. ... Which is more statistically powerful? ...
    (sci.stat.edu)
  • Paired t test vs. 2-way ANOVA
    ... run 2-way ANOVA with two factors, one factor fixed with two levels while ... the other factor being random (no repeated measure for each cell): ... but I could not prove it by comparing s^2 and MSAB algebraically. ... Which is more statistically powerful? ...
    (sci.stat.math)